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Integral Calculus> evaluate the following integral ∫ cos 2x ...

question mark

evaluate the following integral
∫ cos 2x / (cos x + sin x)^2 dx

taniska , 11 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:
Hello student,
Please find the answer to your question below

$I = \int \frac{cos2x}{(cosx+sinx)^2}dx$
$I = \int \frac{cos2x}{(cos^{2}x+sin^{2}x+2sinxcosx)}dx$
$I = \int \frac{cos2x}{(1+sin2x)}dx$
$1+sin2x = t$
$2cos2xdx = dt$
$I = \frac{1}{2}\int \frac{dt}{t}$
$I = \frac{1}{2}log(t) + c$
$I = \frac{1}{2}log(1+sin2x) + c$

Last Activity: 11 Years ago

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